Question $3.$ Colin$$s corporation has a perpetual stream of EBIT equal to $$250$m per year. The

cost of capital for the unlevered firm is $12\%.$ The firm incurs $$30$m of interest payments for the

perpetual bonds it has issued. The cost of debt is $6\%.$ The corporate tax rate is $40\%.(20$ marks$)$

a$)$ What is the value of the unlevered firm? $(3$ marks$)$

b$)$ What is the value of the levered firm? $(6$ marks$)$

c$)$ What is the value of equity of the firm if D$/$E is $0\mathrm{.}35?(6$ marks$)$

d$)$ If the levered beta of the firm is $1\mathrm{.}5,$ what is its unlevered beta? $(2$ marks$)$

e$)$ If the D$/$E of the firm increases from $0\mathrm{.}35$ to $0\mathrm{.}65,$ how does the levered beta changes

$($compare to $$d$)?$ How do you explain this change? $(3)$